2019 • Other
Averaging Symmetric Positive-Definite Matrices
Authors:
Yuan, Xinru,
Huang, Wen,
Absil, Pierre-Antoine ,
Gallivan, Kyle A.
Published in:
Hanbook of Variational Methods for Nonlinear Geometric Data and applications
Symmetric positive definite (SPD) matrices have become fundamental computational objects in many areas, such as medical imaging, radar signal processing, and mechanics. For the purpose of denoising, resampling, clustering or classifying data, it is often of interest to average a collection of symmetric positive definite matrices. This paper reviews and proposes different averaging techniques for symmetric positive definite matrices that are based on Riemannian optimization concepts.